Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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429 views

What is the intuition behind a positive theta for European long puts?

I've googled extensively for an answer to this question. Very similar (if not identical) questions have popped up in this same website (example) but I never find the answers to be clear and/or precise....
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N-period state price deflators

Given that the non-dividend paying share is at $5. In each 6 future 6 month period its value can either rise by 25% or fall by 10%. The continuously compounded risk free rate is 5% p.a. Consider a ...
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1 answer
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Confusion Regarding Dynamically Delta Hedging a Short Option

To my understanding, market makers (mm) in the options market dynamically delta-hedge their portfolios by buying/shorting the underlying, thus eliminating directional risk and profiting from providing ...
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2 votes
1 answer
239 views

Data source for FX options

I have daily quotes for the new york and london fixings of fx options on EURUSD. I can choose between two sources: BGN and CMPN. Apparently these are based on slightly different methods of aggregating ...
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2 answers
210 views

FX option quotation in interbank market

I am looking at the different ways in which FX options (say EUR/USD option) are quoted in interbank markets. Is it quoted using the option chain? I also saw a piece where it is said that it is quoted ...
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61 views

Is there an analogous strikeFromDelta implementation for 1st gen barrier options?

I have a simple replication pricing implementation for 1st gen exotics (digitals, single and double barriers, etc.). In order to effectively test strategies I want to price "like" strikes ...
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182 views

What is the probability of touching point A first?

The probability of a stock touching a point A which is below the current spot price is 35%, and the probability of the stock touching a point B which is above the current spot price is 20%. How can I ...
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3 votes
0 answers
64 views

CMS cap has more vega exposure than CMS floor for same strike

When I priced a 10y expiry single look CMS30 ATMF CAP, I noticed that the vega exposure is higher than that of the same 10y expiry single look CMS30 ATMF FLOOR. Why is that? I have a suspicion that it ...
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Unitise an options portfolio

Suppose I have a portfolio of European index options (long call, short put) and risk free assets (buy bank bills) to create a synthetic long index position. I wish to unitise this portfolio to ...
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1 answer
207 views

What is delta of an option signaling?

In an interview I was once asked what the delta of an option was and my answer started from the fact that it is the first derivative of the option with respect to the price, and then I concluded ...
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1 answer
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Alternatives to RDBMS for options backtesting

I've assembled a large dataset (~2B+ records) of options price data in MySQL for backtesting purposes. At a number of points, due to the sheer amount of data being retrieved and filtered, processing ...
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4 votes
1 answer
227 views

How is Emanuel Derman's implied tree model implied volatility skew derived?

I am reading Emanuel Derman's paper Patterns of Volatility Change. The section, Implied Volatility In The Sticky Implied Tree Model has the linear skew approximation near the old underlying $S_0$ $$\...
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1 vote
0 answers
135 views

Using delta as probability of an option expiring in the money

I understand that delta can be seen as a probability proxy for an option expiring in the money, as well as deltas for call options ranging from 0 to 1 and deltas for put options ranging from 0 to -1. ...
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1 answer
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Reference for path dependent options

I want to study path dependent options for which I am following the book Paul Wilmott on Quantitative finance.But here I dont find the detailed explanations or derivations for the various PDEs .So is ...
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1 answer
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Difference in pricing of American call and put

In Paul Wilmotts quantitative finance books he says that the the value of an American option satisfies the following $$ \frac{\partial V}{\partial t}+\frac{1}{2}\sigma^2S^2 \frac{\partial^2V}{\partial ...
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3 votes
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Independent variable in pricing of strongly path dependent options

I am reading Paul Wilmott on quantatative finance where he discuss the pricing of strongly path dependent options.The payoff at expiry T depends on the path taken by the asset in the sense that it ...
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1 answer
749 views

How to derive the relationship between gamma and theta?

I am trying to derive this formula Θ = –0.5 × Γ × S^2 × σ^2 to see where it comes from. My thinking is that PnL = delta dS + Vdσ + 0.5Γ(dS)^2 + Θdt. Assume we delta hedged and vega hedged, first and ...
2 votes
0 answers
53 views

MOC or TAS mechanism to trade stock options?

Wonder if anyone can help. Is there a product or mechanism to trade cleared stock options at the settlement price, in the same manner to Market on Close orders or Trade at Settle on commodity markets?...
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1 answer
52 views

Computing the denominator of diluted earnings per share

I'm practicing for CFA level 1, and I faced this question. I don't understand the last part (802 − 481 = 321) because I understand that a company doesn't realize options of its own shares, if you are ...
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839 views

What does it mean to be long the skew?

Consider an equity option such as SPY and I'm long the skew, do I make money if puts raise in price and calls decrease or the opposite?
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2 answers
189 views

How is delta defined as a unit?

This is going to be a embarrassingly basic question. But the answer seems to be hard to find. What does, say, selling, $d$ delta of calls mean? How is the "delta" defined? I am not asking ...
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2 votes
0 answers
67 views

Best way to measure time to expiration for options?

From my reading it seems that only trading days should be accounted for when calculating time to expiration. On the other hand, I see that VIX is calculated using every day until expiration without ...
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1 vote
1 answer
164 views

Early exercise American Options with Dividend

this is a basic question but I have not fully understood it. Let's say we have dividend paying stock (continuous dividend yield), when would we exercise the Option early? Since the Dividend yield is ...
2 votes
1 answer
209 views

Question about pricing forward start option with Heston Monte Carlo

I'm trying to price a forward start option with payoff $\Big(\dfrac{S_{T_2}}{S_{T_1}}-1\Big)^+$ with Heston Monte Carlo. Heston Model: $$ dS_t = rS_tdt + \sqrt{v_t}S_tdW_t^1$$ $$ dv_t = \kappa(m-v_t) +...
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1 answer
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Montecarlo pricing

I have some problems with the Montecarlo simulation to price a generic Call option. I want to explain something regarding MC simulation with a simple cases, and after that I am going to talk about my ...
4 votes
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127 views

Delta hedging the day before expiry

In practice, how do people usually delta hedge options the day before expiry? Would you still use the black Scholes delta and then close out the position in the underlying immediately after expiry? ...
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2 votes
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Equivalence of expectation condition for contingent claims attainable and contingent claims super replicable

We have the following definitions for set of contingent claims attainable and contingent claims super replicable I want to prove the following result How do I show iii $\implies $ ii.I understand ...
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Better to "work order" or just give best limit price when placing multi-leg option orders through IB with SMART routing

I place option trades usually consisting of 2-4 legs...mostly ratios spreads through IB using the SMART routing algorithm. Say for a particular trade, the bid is 0.04 debit and the ask is 0.17 debit. ...
2 votes
1 answer
214 views

No free lunch with bounded and vanishing risk

I am reading a book which states 'No free lunch with bounded risk as follows where $\tilde{V}_t$ is the discounted value of the portfolio.Then it states the following theorem EMM is the equivalent ...
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6 votes
1 answer
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Vol, Gamma, Vega -- essentially all the same?

When talking to traders I hear this sentence a lot I am a buyer/seller of X where X = {vol, gamma, vega} Is X basically all the same -- they are just saying -- I think implied volatility is cheap or ...
8 votes
1 answer
488 views

Path-dependent options valuation

Assume that we have an arbitrage-free and complete market. The well known formula for the arbitrage-free price of an attainable derivative $X$ at time $0 \leq t \leq T$ is given by: \begin{align*} V(t)...
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2 votes
1 answer
260 views

Proving the discounted stock price is martingale

Let $\mathcal{K}_s$ be $$ \mathcal{K}_s=\{\tilde{V}_t(\theta):0\leq t<\infty,\,\theta\text{ a simple strategy}\},$$ where $\tilde{V}_t(\theta)$ is the discounted value process of the self financing ...
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1 vote
2 answers
202 views

Rationale for the CMS Spread and CMS Rate as being underlying for Dual Range Accrual?

I was searching on the products issued by the banks to retail investors, and saw some of the Dual Range Accruals having underlying as USD CMS 30Y - 2Y, and USD CMS 10Y, each having low barrier and ...
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3 votes
1 answer
549 views

Why is gamma exposed through the square of spot prices?

As per this article, "the mathematically intuitive way to expose gamma is through the square of the underlying price": https://llllvvuu.dev/blog/unbundling-gamma Can someone explain this? ...
2 votes
0 answers
110 views

Net delta and gamma profile of a put spread

I have a question regarding the description in Simon Gleadall's book -- option gamma trading which you can find a copy HERE. The following paragraph he discussed about gamma and delta profile of a ...
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Why a long-dated option has delta > 0.5?

Each option book states that the delta, considered as the hedge ratio and not the probability to have the option exercised, is 50% for ATM options. Anyway, empirically speaking I see it is more than ...
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123 views

FX options: is convexity usually heavily overpriced?

I have access to daily vol quotes for EURUSD options from 2006 to today. I was playing around with them and constructed a "daily rolled backtest" for various options constructs, like ...
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5 votes
1 answer
432 views

Is publication of Black-Scholes in 1973 and founding of CBEO in 1973 coincidental?

Apparently, CBOE was founded in 1973 and opened on 1st January that year (source = Google), to start trading listed options. The famous Black-Scholes paper was published also in 1973. I am wondering ...
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1 answer
216 views

Historical Options data

Are there any good sources where I can obtain daily historical options data (strike price, expiration dates, bid/ask spread, etc). I understand that this type of data is very hard to come by and ...
0 votes
2 answers
151 views

Early expiry option implied volatility

I’m new to this forum so first of all I wanna welcome everyone here. I am a commodity trader, mostly covering option books (vanilla and structured one) and I would ask more expert people how they can ...
-1 votes
1 answer
298 views

Question in convex arbitrage [closed]

In convex arbitrage, we say that if the convexity of call(put) price as a function of the strike is violated, we can have arbitrage strategy. For instance, $$ C_{K_2}\geq \lambda C_{K_1}+(1-\lambda) ...
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1 answer
93 views

What happens when you buy call options on a stock that does a stock split

suppose i say lyft in 2023 will be worth more then 50 per share (the current call price for the option). suppose im right and each share is worth 75, but in the interim lyft announces a 2-1 stock ...
3 votes
0 answers
71 views

Model independent (or reasonable assumption) bounds on OTM put price given an ATM call price

I am looking for model independent (or weak/reasonable assumption) bounds on price of a OTM vanilla put on strike $k1$, conditional on an observable price for a ATM call at some strike $k2$. I ...
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2 votes
2 answers
573 views

Relationship between VIX and Vega

Assuming that all other factors (such as underlying price, strike price, etc.) remain unchanged, I want to see how a spike in VIX would affect the price of the average call option? Assume Vega is ...
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1 vote
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How to measure accuracy of SABR volatility surfaces?

I would like to test how accurate are SABR volatility surfaces with respect to historical volatility over a given time period and for a specific equity index. Reading a few papers I realised that one ...
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0 answers
44 views

What happens to options on a SPACs unit class post deal closure?

SPAC unit share classes are typically structured as following: Unit = Stock + (1/5) Warrant When the SPAC deal closes the ticker changes and the unit converts to ...
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2 votes
0 answers
33 views

How to derive Parameter Derivative within an FFT integral

I have the following function (Carr-Madan) of which I am trying to take the derivative wrt $\theta$: $c(k)=\int_0^\infty \frac{e^{-iuk}}{\alpha^2 + \alpha - u^2 + i(2\alpha+1)u} e^{\phi_T(u-(\alpha+1)...
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1 vote
0 answers
69 views

Compare rich / cheap options on 2 underlyings

this question can turn out to be very basic but its something that has been bugging me. Say I want to buy/sell an option on A vs sell/buy an option on B. Facts I know A and B are different ...
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85 views

Is there an equation that gives you the optimal spread width or strike prices when opening a vertical options spread?

On a specific leg, when going to open a spread is there an equation that can tell me at what strike price I should sell at and what strike price I should buy at? I look at this options calculator ...
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Finite Difference Method in Greeks (Options)

I need a way to approximate the analytical formula of Greeks of a generic call option using the Finite Difference Method. For example, the FD method for Delta/Gamma is the following one: Now, I am in ...

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